Numerical methods for hybrid control and chance-constrained optimization problems.

Keywords. Optimal control, Hybrid systems, Numerical schemes, Stochastic optimization, Chance constraint, Space launchers

Abstract. This thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistic techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold.